In this dissertation, we examine mechanics of rhythmic tracheal compression (RTC) in the darkling beetle, Zophobas morio. In Chapter 2, we studied the relationship between hemolymph pressure and tracheal collapse to test the hypothesis that pressure is a driving mechanism for RTC. We found that tracheae collapse as pressure increases, but other physiological factors in the body may be affecting tracheal compression in live beetles. Additionally, as the tracheae compress, they do so in varying spatial patterns across the insect body. In chapter 3, we examined spatial variations in the taenidial spacing, stiffness, and tracheal thickness along the length of the tracheae. We related variations in Young's modulus and taenidial spacing with measurements of collapse dimples and found that spatial patterns of Young's modulus correlate with dimensions of collapse dimples. This correlation suggests an intuitive link between tracheal stiffness variations and the unique patterns observed in compressing tracheae. Lastly, in chapter 4, we studied the non-uniform collapse patterns in 3-D. By manually pressurizing the hemocoel and imaging using synchrotron microcomputed tomography (SR-µCT), we reconstructed the tracheal system in its compressed state. While previous studies used 2-D x-ray images to examine collapse morphology, ours is the first to quantify collapse patterns in 3-D and compare with previous 2-D quantification methods. Our method is also the first to make a direct measure of tracheal volume as the tracheal system compresses, similar to the phenomenon that occurs during rhythmic tracheal compression. / Doctor of Philosophy / Insects have long been a source of curiosity and inspiration for scientists and engineers. The insect respiratory system stands as an example of a seemingly complex oxygen delivery system that operates with relative simplicity. As opposed to mammals and other vertebrates, the insect respiratory system does not deliver oxygen using blood. Instead, insects possess a massive network of hollow tracheal tubes that are distributed throughout the body. Air enters spiracular valves along the length of the insect body, travels through the tracheal tube network, and is delivered directly to the tissues. In some insects, the tracheae compress and expand, driving flow of respiratory gasses. However, unlike vertebrate lungs, there are no muscles directly associated with the tracheal system that would drive this tracheal compression, and exactly how this behavior occurs is not fully understood. In this dissertation, we examined pulsatory increases in blood pressure as a possible mechanism that underlies these tracheal compressions in the darkling beetle, Zophobas morio. Additionally, as the tracheae compress, they do so with varying spatial patterns across the insect body. Because tracheae are complex and non-uniform composite tubes, we examined spatial variations in the microstructure, stiffness, and tracheal thickness along the length of the trachea. Lastly, we visualized the variable collapse patterns in three dimensions using synchrotron micro-computed tomography combined with manual pressurization of the hemocoel. While previous studies used two-dimensional x-ray images to quantify tracheal collapse patterns, this work represents the first three-dimensional study. Understanding tracheal collapse mechanics, material properties, and their relationships with the circulatory system can help to gain an understanding of how insects create complex fluid flows within the body using relatively simple mechanisms.

Hydroplaning is a phenomenon that occurs when a layer of water between the tire and pavement pushes the tire upward. The tire detaches from the pavement, preventing it from providing sufficient forces and moments for the vehicle to respond to driver control inputs such as breaking, accelerating and steering. This work is mainly focused on the tire and its interaction with the pavement to address hydroplaning. Before using a full-scale tire model, interactions of the tread block with a specific surface is studied. To do so, several mechanical tests such as uniaxial, biaxial, planar (shear), and DMA are conducted to predict the hyper-viscoelastic properties of the rubber. Using multi-scale modeling techniques, the friction coefficient between the tire and pavement, for wet conditions, is characterized via developing 2D and 3D model representing the rubber tread interacting with the rough surface. Using a tire model that is validated based on results found in the literature as well as in-house experimental data, fluid-structure interaction (FSI) between the tire-water-road surfaces are investigated through two approaches. In the first approach, the coupled Eulerian-Lagrangian (CEL) formulation was used. The drawback associated with the CEL method is the laminar assumption that the behavior of the fluid at length scales smaller than the smallest element size is not captured. To improve the simulation results, in the second approach, an FSI model incorporating finite-element methods and the Navier-Stokes equations for a two-phase flow of water and air, and the shear stress transport k-ω turbulence model, was developed and validated, improving the prediction of real hydroplaning scenarios. The improved FSI model was applied to hydroplaning speed and cornering force scenarios. In addition, tire contact patch length was calculated using the developed FSI model and was compared to the results obtained from the intelligent tire. / Doctor of Philosophy / Hydroplaning is a phenomenon that occurs when a layer of water between the tire and pavement pushes the tire upward. The tire detaches from the pavement, preventing it from providing sufficient forces and moments for the vehicle to respond to driver control inputs such as breaking, accelerating and steering. Hydroplaning as well as low skid resistance are considered as the main factors leading to traffic accidents. This work is mainly focused on the tire and its interaction with the pavement to address hydroplaning. Different factors involve in the hydroplaning phenomenon such as water film thickness, tire pressure, tire tread pattern, tire tread depth, vehicle speed and pavement texture. Before using a full-scale tire model, interactions of the tire tread with a specific surface is studied. To do so, several mechanical tests are conducted to predict the hyper-viscoelastic properties of the rubber. Using a single scale methodology is not capable to obtain the sufficient information regarding the effect of roughness on the friction. As a result, using multi-scale modeling techniques, the friction coefficient between the tire and pavement, for wet conditions, is characterized via developing 2D and 3D model representing the rubber tread interacting with the rough surface. Since in the hydroplaning problem, a solid structure and a fluid domain are in interaction, such a problem considered as a fluid-structure interaction (FSI) problem. In this work, the FSI between the tire-water-road surfaces are investigated through two approaches. To improve the simulation results, an FSI model incorporating finite-element methods and the Navier-Stokes equations for a two-phase flow of water and air, and the shear stress transport k-ω turbulence model, was developed and validated, improving the prediction of real hydroplaning scenarios. In addition, tire contact patch length was calculated using the developed FSI model and was compared to the results obtained from the intelligent tire.

Novel aircraft configurations tend to be sized by physical phenomena that are largely neglected during conventional fixed wing aircraft design. High-fidelity fluid-structure interaction that accurately models geometric nonlinerity during a transient aeroelastic gust response is critical for sizing the aircraft configuration early in the design process. The primary motivation of this research is to develop a continuum shape sensitivity method that can support gradient-based design optimization of practical and multidisciplinary high-fidelity analyses. A local continuum sensitivity analysis (CSA) that utilizes spatial gradient reconstruction (SGR) and avoids mesh sensitivities is presented for shape design derivative calculations. Current design sensitivity analysis (DSA) methods have shortcomings regarding accuracy, efficiency, and ease of implementation. The local CSA method with SGR is a nonintrusive and element agnostic method that can be used with black box analysis tools, making it relatively easy to implement. Furthermore, it overcomes many of the accuracy issues documented in the current literature. The method is developed to compute design derivatives for a variety of applications, including linear and nonlinear static beam bending, linear and nonlinear transient gust analysis of a 2-D beam structure, linear and nonlinear static bending of rectangular plates, linear and nonlinear static bending of a beam-stiffened plate, and two-dimensional potential flow. The analyses are conducted using general purpose codes. For each example the design derivatives are validated with either analytic or finite difference solutions and practical numerical and modeling considerations are discussed. The local continuum shape sensitivity method with spatial gradient reconstruction is an accurate analytic design sensitivity method that is amenable to general purpose codes and black box tools. / Ph. D.

This work presents a partitioned approach to simulating free-surface flow interaction with hyper-elastic structures in which a smoothed particle hydrodynamics (SPH) solver is coupled with a finite-element (FEM) solver. SPH is a mesh-free, Lagrangian numerical technique frequently employed to study physical phenomena involving large deformations, such as fragmentation or breaking waves. As a mesh-free Lagrangian method, SPH makes an attractive alternative to traditional grid-based methods for modeling free-surface flows and/or problems with rapid deformations where frequent re-meshing and additional free-surface tracking algorithms are non-trivial. This work continues and extends the earlier coupled 2D SPH-FEM approach of Yang et al. [1,2] by linking a double-precision GPU implementation of a 3D weakly compressible SPH formulation [3] with the open source finite element software Code_Aster [4]. Using this approach, the fluid domain is evolved on the GPU, while the CPU updates the structural domain. Finally, the partitioned solutions are coupled using a traditional staggered algorithm. / Ph. D.

Current Federal Aviation Regulations require costly and time consuming crashworthiness testing to certify aircraft. These tests are only capable of a limited assessment of progressive damage and all crash configurations and scenarios cannot be physically evaluated. Advancements in technology have led to accurate and effective developments in numerical modeling that have the possibility of replacing these rigorous physical experiments. Through finite element analysis, an in-depth investigation of an aircraft equipped with a fabricated composite undercarriage was evaluated during water ditching. The severe impact of aircraft ditching is dynamic and nonlinear in nature; the goal of this work to develop a methodology that not only captures the structural response of the aircraft, but also the fluidic behavior of the water. Fundamental studies were first conducted on a well-researched fluid-solid interaction problem, the water entry of a wedge. Typical modeling strategies did not capture the desired detail of the event. An advanced meshing scheme combining meshed and meshless Lagrangian techniques was developed and multiple wedge angles were tested and compared to analytic and qualitative results. The meshing technique proved valid, as the difficult to model phenomena of splashing was captured and the maximum impact force was within five percent of analytical calculations for the 20° and 30° deadrise wedge. Physical small scale aircraft ditching experiments were then performed with an innovative testing platform capable of producing varied aircraft approach configurations. The model was outfitted with an instrumented composite undercarriage to record data throughout the impact while a high-speed camera recorded the event. Numerical simulations of the model aircraft were then compared to experimental results with a strong correlation. This methodology was then ultimately tested on a deformable model of a fuselage section of a full-size aircraft. / Master of Science

The method of Continuum Sensitivity Analysis (CSA) with Spatial Gradient Reconstruction (SGR) is presented for calculating the sensitivity of fluid, structural, and coupled fluid-structure (aeroelastic) response with respect to shape design parameters. One of the novelties of this work is the derivation of local CSA with SGR for obtaining flow derivatives using finite volume formulation and its nonintrusive implementation (i.e. without accessing the analysis source code). Examples of a NACA0012 airfoil and a lid-driven cavity highlight the effect of the accuracy of the sensitivity boundary conditions on the flow derivatives. It is shown that the spatial gradients of flow velocities, calculated using SGR, contribute significantly to the sensitivity transpiration boundary condition and affect the accuracy of flow derivatives. The effect of using an inconsistent flow solution and Jacobian matrix during the nonintrusive sensitivity analysis is also studied. Another novel contribution is derivation of a hybrid adjoint formulation of CSA, which enables efficient calculation of design derivatives of a few performance functions with respect to many design variables. This method is demonstrated with applications to 1-D, 2-D and 3-D structural problems. The hybrid adjoint CSA method computes the same values for shape derivatives as direct CSA. Therefore accuracy and convergence properties are the same as for the direct local CSA. Finally, we demonstrate implementation of CSA for computing aeroelastic response shape derivatives. We derive the sensitivity equations for the structural and fluid systems, identify the sources of the coupling between the structural and fluid derivatives, and implement CSA nonintrusively to obtain the aeroelastic response derivatives. Particularly for the example of a flexible airfoil, the interface that separates the fluid and structural domains is chosen to be flexible. This leads to coupling terms in the sensitivity analysis which are highlighted. The integration of the geometric sensitivity with the aeroelastic response for obtaining shape derivatives using CSA is demonstrated. / Ph. D.

This dissertation presents useful nonlinear models for fluid forcing on a moving body in two distinct contexts, and methods for analyzing the geometric structure within those and other mathematical models. This manuscript style dissertation presents three works within the theme of understanding fluid forcing and geometric structure. When a bluff body is free to move in the presence of an incoming bluff body wake, the average forcing on the body is dependent on its position relative to the upstream bluff body. This position-dependent forcing can be conceptualized as a stiffness, much like a spring. This work presents an updated model for the quasi-steady fluid forcing of a wake and extends the notion of wake stiffness to consider a nonlinear spring. These results are compared with kinematic experimental results to provide an example of the application of this framework. Fluid force models also play a role in understanding the behavior of passive aerodynamic gliders, such as gliding animals or plant material. The forces a glider experiences depend on the angle that its body makes with respect to its direction of motion. Modeling the glider as capable of pitch control, this work considers a glider with a fixed angle with respect to the ground. Within this model, all trajectories in velocity space collapse to a 1-dimensional invariant manifold known as the terminal velocity manifold. This work presents methods to identify the terminal velocity manifold, investigates its properties, and extends it to a 2-dimensional invariant manifold in a 3-dimensional space. Finally, in the search for manifolds such as the terminal velocity manifold, this dissertation introduces a new diagnostic for identifying the low dimensional geometric structure of models. The trajectory divergence rate uses instantaneous vector field information to identify regions of large normal stretching and strong normal convergence between nearby invariant manifolds. This work lays out the mathematical basis of the trajectory divergence rate and shows its application to approximate a variety of structures including slow manifolds and Lagrangian coherent structures. This dissertation applies nonlinear theoretical and numerical techniques to analyze models of fluid forcing and their geometric structure. The tools developed in this dissertation lay the groundwork for future research in the fields of flow-induced vibration, plant and animal biomechanics, and dynamical systems. / Ph. D. / When an object moves through a fluid such as air or water, the motion of the surrounding fluid generates forces on the moving object, affecting its motion. The moving object, in turn, affects the motion of the surrounding fluid. This interaction is complicated, nonlinear, and hard to even simulate numerically. This dissertation aims to analyze simplified models for these interactions in a way that gives a deeper understanding of the physics of the interaction between an object and a surrounding fluid. In order to understand these interactions, this dissertation looks at the geometric structure of the models. Very often, there are low-dimensional points, curves, or surfaces which have a very strong effect on the behavior of the system. The search for these geometric structures is another key theme of this dissertation. This dissertation presents three independent studies, with an introduction and conclusion to discuss the overall themes. The first work focuses on the forces acting on a cylinder in the wake of another cylinder. These forces are important to understand, because the vibrations that arise from wake forcing are important to consider when designing bridges, power cables, or pipes to carry oil from the ocean floor to offshore oil platforms. Previous studies have shown that the wake of a circular cylinder acts like a spring, pulling harder on the downstream cylinder the more it is moved from the center of the wake. In this work, I extend this idea of the wake as a spring to consider a nonlinear spring, which keeps the same idea, but provides a more accurate representation of the forces involved. The second work considers a simple model of gliding flight, relevant to understanding the behavior of gliding animals, falling leaves, or passive engineered gliders. Within this model, a key geometric feature exists on which the majority of the motion of the glider occurs, representing a 2-dimensional analogy to terminal velocity. In this work, I study the properties of this influential curve, show several ways to identify it, and extend the idea to a surface in a 3-dimensional model. The third study of this dissertation introduces a new mathematical quantity for studying models of systems, for fluid-body interaction problems, ocean flows, chemical reactions, or any other system that can be modeled as a vector field. This quantity, the trajectory divergence rate, provides an easily computed measurement of highly attracting or repelling regions of the states of a model, which can be used to identify influential geometric structures. This work introduces the quantity, discusses its properties, and shows its application to a variety of systems.

Fluid-structure interaction (FSI) is an important physical phenomenon in many applications and across various disciplines including aerospace, civil and bio-engineering. In civil engineering, applications include the design of wind turbines, pipelines, suspension bridges and offshore platforms. Ocean structures such as drilling risers, mooring lines, cables, undersea piping and tension-leg platforms can be subject to strong ocean currents, and such structures may suffer from Vortex-Induced Vibrations (VIV's), where vortex shedding of the flow interacts with the structural properties, leading to large amplitude vibrations in both in-line and cross-flow directions. Over the past years, many experimental and numerical studies have been conducted to comprehend the underlying physical mechanisms. However, to date there is still limited understanding of the effect of oscillatory interactions between fluid flow and structural behavior though such interactions can cause large deformations. This research proposes a mathematical framework to accurately predict FSI for elastically supported rigid structures. The numerical method developed solves the Navier-Stokes (NS) equations for the fluid and the Equation of Motion (EOM) for the structure. The proposed method employs Finite Differences (FD) on Cartesian grids together with an improved, efficient and oscillation-free Immersed Boundary Method (IBM), the accuracy of which is verified for several test cases of increasing complexity. A variety of two and three dimensional FSI simulations are performed to demonstrate the accuracy and applicability of the method. In particular, forced and a free vibration of a rigid cylinder including Vortex-Induced Vibration (VIV) of an elastically supported cylinder are presented and compared with reference simulations and experiments. Then, the interference between two cylinders in tandem arrangement at two different spacing is investigated. In terms of VIV, three different scenarios were studied for each cylinder arrangement to compare resonance regime to a single cylinder. Finally, the IBM is implemented into a three-dimensional Large-Eddy Simulation (LES) method and two high Reynolds number (Re) flows are studied for a stationary and transversely oscillating cylinder. The robustness, accuracy and applicability of the method for high Re number flow is demonstrated by comparing the turbulence statistics of the two cases and discussing differences in the mean and instantaneous flows.

Fluid-structure interaction (FSI) is an interesting and challenging interdisciplinary area comprised of fields such as engineering- fluids/structures/solids, computational science, and mathematics. FSI has several practical engineering applications such as the design of coastal infrastructure (such as bridges, levees) subjected to harsh environments from natural forces such as tsunamis, storm surges, etc. Development of accurate input conditions to more detailed and complex models involving flexible structures in a fluid domain is an important requirement for the solution of such problems. FSI researchers often employ methods that use results from physical wave basin experiments to assess the wave forces on structures. These experiments, while closer to the physical phenomena, often tend to be time-consuming and expensive. Experiments are also not easily accessible for conducting parametric studies. Alternatively, numerical models when developed with similar capabilities will complement the experiments very well because of the lower costs and the ability to study phenomena that are not feasible in the laboratory. This dissertation is aimed at contributing to the solution of a significant component of the FSI problem with respect to engineering applications, covering accurate input to detailed models and a numerical wave basin to complement large-scale laboratory experiments. To this end, this work contains a description of a three-dimensional numerical wave tank (3D-NWT), its enhancements including the piston wavemaker for generation of waves such as solitary, periodic, and focused waves, and validation using large-scale experiments in the 3D wave basin at Oregon State University. Performing simulations involving fluid dynamics is computational-intensive and the complexity is magnified by the presence of the flexible structure(s) in the fluid domain. The models are also required to take care of large-scale domains such as a wave basin in order to be applicable to practical problems. Therefore, undertaking these efforts requires access to high-performance computing (HPC) platforms and development of parallel codes. With these objectives in mind, parallelization of the 3D-NWT is carried out and discussed in this dissertation. / Graduation date: 2011

A monolithic approach to aero-structural analysis and optimization has been developed and implemented. In contrast to a partitioned approach which uses individual fluid and structural solvers to solve their respective systems separately, the monolithic approach solves a fully-coupled system simultaneously, enforcing solution compatibility across the sub-system interfaces at each iteration. In this work, a three-field formulation is used, consisting of fluid, structural, and fluid mesh-movement sub-systems. The performance of the monolithic approach is characterized using 1-D unsteady and 2-D steady analysis problems, and compared with a partitioned approach. Four steady model aero-structural optimization problems are also investigated. Gradients of the objective function are computed using the discrete-adjoint and flow-sensitivity (direct) methods. In each case, the monolithic approach is shown to be a promising option for efficient aero-structural analysis and optimization, though the implementation requires additional development of coupling sub-matrices when compared to a partitioned approach.